
By definition of the Lie bracket, one can obtain [1]}
\(\left[\bar{\lambda },\bar{\eta }\right]_{\bar{{\cal X}}} = \mathrm {D}\bar{\eta }\left(\bar{{\cal X}}\right)\left[\bar{\lambda }_{\bar{{\cal X}}}\right]- \mathrm {D}\bar{\lambda }\left(\bar{{\cal X}}\right)\left[\bar{\eta }_{\bar{{\cal X}}}\right].\) 
